Abstract:

The full-length book provides a mathematical framework for decision making and the analysis of (consequential) hidden risks, those tail events undetected or improperly detected by statistical machinery; and substitutes fragility as a more reliable measure of exposure. Model error is mapped as risk, even tail risk.

Risks are seen in tail events rather than in the variations; this necessarily links them mathematically to an asymmetric response to intensity of shocks, convex or concave.

The difference between “models” and “the real world” ecologies lies largely in an additional layer of uncertainty that typically (because of the same asymmetric response by small probabilities to additional uncertainty) thickens the tails and invalidates all probabilistic tail risk measurements – models, by their very nature of reduction, are vulnerable to a chronic underestimation of the tails.

So tail events are not measurable; but the good news is that exposure to tail events is. In “Fat Tail Domains” (Extremistan), tail events are rarely present in past data: their statistical presence appears too late, and time series analysis is similar to sending troops after the battle. Hence the concept of fragility is introduced: is one vulnerable (i.e., asymmetric) to model error or model perturbation (seen as an additional layer of uncertainty)?

Part I looks at the consequences of fat tails, mostly in the form of slowness of convergence of measurements under the law of large number: some claims require 400 times more data than thought. Shows that much of the statistical techniques used in social sciences are either inconsistent or incompatible with probability theory. It also explores some errors in the social science literature about moments (confusion between probability and first moment, etc.)

Part II proposes a more realistic approach to risk measurement: fragility as nonlinear (concave) response, and explores nonlinearities and their statistical consequences. Risk management would consist in building structures that are not negatively asymmetric, that is both “robust” to both model error and tail events. Antifragility is a convex response to perturbations of a certain class of variables.

Number of Pages in PDF File: 296

Keywords: Risk Management, Probability Theory

via Silent Risk: Lectures on Fat Tails, (Anti)Fragility, and Asymmetric Exposures by Nassim Nicholas Taleb :: SSRN.